Question

Which statement is not correct regarding the neutral axis of a beam (of a linear-elastic material) in pure bending?

The deflection of the neutral axis is zero.

The normal strain at the neutral axis is zero.

The neutral axis passes through the centroid of the section.

The normal stress at the neutral axis is zero.

Answer 1

The deflection of the neutral axis is not zero in pure bending of a beam of a linear-elastic material.

Step-by-step explanation:

The statement that is not correct regarding the neutral axis of a beam (of a linear-elastic material) in pure bending is: The deflection of the neutral axis is zero.

In pure bending, a beam undergoes deformation and the neutral axis is the line that experiences no change in length. However, the neutral axis does have a deflection since it is a curved line. The amount of deflection depends on the magnitude of the bending moment and the properties of the material.

Therefore, the correct option is that the deflection of the neutral axis is not zero in pure bending.

Answer 2

The correct answer is: The normal stress at the neutral axis is zero.

The statement "The normal stress at the neutral axis is zero" is not correct regarding the neutral axis of a beam in pure bending. In pure bending, the neutral axis experiences pure bending stress, which is a combination of tensile and compressive stresses.

The normal stress at the neutral axis is not zero; it is, in fact, zero at the centroid of the section. So, the correct answer is: The normal stress at the neutral axis is zero. The neutral axis is an axis within the beam's cross-section where the material experiences only elastic deformation without any change in length. At the neutral axis, the fibers neither stretch nor compress; hence, the strain is zero at this location.